QCD factorization for the four-body leptonic B-meson decays

Abstract

Employing the QCD factorization formalism we compute $$ {B}_u^{-}\to {\gamma}^{\ast}\mathrm{\ell}{\overline{v}}_{\mathrm{\ell}} $$ B u − → γ ∗ ℓ v ¯ ℓ form factors with an off-shell photon state possessing the virtuality of order mb ΛQCD and $$ {m}_b^2 $$ m b 2 , respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of mb/ΛQCD in the resulting factorization formulae is subsequently accomplished at next-to-leading logarithmic accuracy with the renormalization-group technique in momentum space. In particular, we derive the soft-collinear factorization formulae for a variety of the subleading power corrections to the exclusive radiative $$ {B}_u^{-}\to {\gamma}^{\ast }{W}^{\ast } $$ B u − → γ ∗ W ∗ form factors with a hard-collinear photon at $$ \mathcal{O}\left({\alpha}_s^0\right) $$ O α s 0 . We further construct a complete set of the angular observables governing the full differential distribution of the four-body leptonic decays $$ {B}_u^{-}\to {\mathrm{\ell}}^{\prime }{\overline{\mathrm{\ell}}}^{\prime}\mathrm{\ell}{\overline{v}}_{\mathrm{\ell}} $$ B u − → ℓ ′ ℓ ¯ ′ ℓ v ¯ ℓ with ℓ, ℓ′ ∈ {e, μ} and then perform an exploratory phenomenological analysis for a number of decay observables accessible at the LHCb and Belle II experiments, with an emphasis on the systematic uncertainties arising from the shape parameters of the leading-twist B-meson light-cone distribution amplitude in heavy quark effective theory.

Precision calculations of the double radiative bottom-meson decays in soft-collinear effective theory

“…In this respect, it remains to be demonstrated evidently that whether the newly proposed method of accessing the nonperturbative light-front quantities with the corresponding equal-time correlation functions calculable on a Euclidean lattice and the standard OPE technique will be able to provide us with phenomenological encouraging results [117]. Third, extending the established strategies of evaluating the factorizable NLP corrections to the factorization analysis for a wide range of exclusive B-meson decays B → γ ν , B → ¯ ν [118] and B → M ν (with M = π, ρ, ω, K ( * ) , D ( * ) ) will be of high interest for probing the delicate strong interaction mechanisms governing a variety of heavy quark decays.…”

Light-cone distribution amplitudes of heavy mesons with QED effects

“…Finally, we remark that the discussion for the inverse-logarithmic moments is not valid for more general moments, as appear for instance in B → γ * ν [14,15], where the moment 1/(ω − n − q − i0) is shifted by the momentum component n − q of the virtual photon. In this case, (2.34) no longer holds and the corresponding RGE does not reduce to a simple form as in (3.7) or (3.22) and (3.23) since such moments cannot be derived from ΦB , given in (3.19), alone.…”

Light-cone distribution amplitudes of heavy mesons with QED effects

“…An analogous equation holds for functions with negative support, so that we obtain the same result for the solution in terms of λ B (µ 0 ) and σ n (µ 0 ) in both cases. Finally, we remark that the discussion for the inverse-logarithmic moments is not valid for more general moments, as appear for instance in B → γ * ν [14,15], where the moment 1/(ω − n − q − i0) is shifted by the momentum component n − q of the virtual photon. In this case, (2.34) no longer holds and the corresponding RGE does not reduce to a simple form as in (3.7) or (3.22) and (3.23) since such moments cannot be derived from ΦB , given in (3.19), alone.…”